Our published patent application WO2005/112806 describes a system for the morcellation of tissue in a minimally invasive procedure. Published patent application WO2008/029092 describes a valve mechanism for use in the morcellating instrument of the earlier application. This valve mechanism helps to ensure that an insufflating gas, used to expand the surgical site to allow for effective access, is constrained within the surgical site, even when a surgical instrument such as a tissue grasper is repeatedly inserted into and retracted from the morcellating instrument. The present invention provides an improvement to this type of arrangement, such that different types of surgical instrument, of different sizes, can be employed within the procedure while still maintaining the insufflating gas within the surgical site.